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Author Hojman, S.A.; Asenjo, F.A.
Title Classical and Quantum Dispersion Relations Type Journal Article
Year 2020 Publication Physica Scripta Abbreviated Journal Phys. Scr.
Volume 95 Issue 8 Pages 7 pp
Keywords Quantum Hamilton-Jacobi equation; Bohm potential; dispersion relation
Abstract It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for non-quantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.
Address [Hojman, Sergio A.] Univ Adolfo Ibanez, Fac Artes Liberales, Dept Ciencias, Santiago 7491169, Chile, Email: sergio.hojman@uai.cl;
Corporate Author Thesis
Publisher Iop Publishing Ltd Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0031-8949 ISBN Medium
Area Expedition Conference
Notes WOS:000543208700001 Approved no
Call Number UAI @ eduardo.moreno @ Serial 1184
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Author Hojman, S.A.; Asenjo, F.A.
Title Dual wavefunctions in two-dimensional quantum mechanics Type Journal Article
Year 2020 Publication Physics Letters A Abbreviated Journal Phys. Lett. A
Volume 384 Issue 13 Pages 5 pp
Keywords Schrodinger equation; Dual solution; Bohm potential; Two-dimensions; Optics
Abstract It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Bohm potential. These solutions can be extended to three-dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two-dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two-dimensional dual wavefunction solutions with an optical (analogue) system. (C) 2020 Elsevier B.V. All rights reserved.
Address [Hojman, Sergio A.] Univ Adolfo Ibanez, Dept Ciencias, Fac Artes Liberales, Santiago 7491169, Chile, Email: sergio.hojman@uai.cl;
Corporate Author Thesis
Publisher Elsevier Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0375-9601 ISBN Medium
Area Expedition Conference
Notes WOS:000525434900002 Approved no
Call Number UAI @ eduardo.moreno @ Serial 1152
Permanent link to this record